Question: Solve for $x$, $ -\dfrac{8}{x} = -\dfrac{7}{x} + \dfrac{5x + 2}{2x} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $x$ $x$ and $2x$ The common denominator is $2x$ To get $2x$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ -\dfrac{8}{x} \times \dfrac{2}{2} = -\dfrac{16}{2x} $ To get $2x$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ -\dfrac{7}{x} \times \dfrac{2}{2} = -\dfrac{14}{2x} $ The denominator of the third term is already $2x$ , so we don't need to change it. This give us: $ -\dfrac{16}{2x} = -\dfrac{14}{2x} + \dfrac{5x + 2}{2x} $ If we multiply both sides of the equation by $2x$ , we get: $ -16 = -14 + 5x + 2$ $ -16 = 5x - 12$ $ -4 = 5x $ $ x = -\dfrac{4}{5}$